A hypergeometric distribution is a decimal that represents the likelihood that W successes will occur within a given sample given that there are X ‘chances’ within the sample (the sample size), Y instances of the successful event in the population as a whole, and Z events in the population.
In short, it is the odds of a person having a certain card in hand. The information from a hypergeometric distribution can be combined with the the information the other player is giving you to help you to determine whether or not he has the card in question (or a similar card).
Let us suppose, for instance, that you are playing an aggressive deck against a more controlling deck. The game is going a little later than you would like… You have reached the 8th turn. Your opponent loves Day of Judgment, so you can be certain his deck contains at least 3 if not 4 of them. He has not played any yet this game. After burning through his chump blockers, you are starting to get in for decent damage. You have a pair of Goblin Guides and a Signal Pest on the field currently. With your opponent at 8 life, you are starting to gain confidence. Unfortunately, you have good reason to fear a Day of Judgment. With your hand clogged with cheap creatures and lands, do you commit more creatures to the battlefield or wait until after the Day of Judgment to continue your assault? Time for some number crunching. Eighth turn. Your opponent was on the draw, so 7+7+2=16 is the number of cards that have been through his hand this game. What is the 2 for, you may ask? He played Divination, so those cards must be taken into account. This gives me the formula: =hypgeomdist(1;16;4;60) [Hint: replace the semicolons with commas if using Excel; I use Google Docs]. The 1 is the number of the particular card in question (day of judgment) we are interested in him/her having. The 16 is the number of cards the player has seen this turn. The 4 is the number of the card (or cards) of interest in the deck. The 60 is the size of the deck. The result is about 0.43, or 43%. This is a reasonably high pobability. Now the question is, what do you think your chances of winning are after he lands a Day of Judgment? If the odds are higher given the hasty creatures you have in hand, your best bet would be to wait it out and get in for damage with the creatures already on the battlefield for the time being. If you know your opponent packs some nasty creatures in his deck that will invariably hit the battlefield after he blows up the board, giving you almost zero chances of winning, you will need to press your advantage and hope that it is enough.
I will try to get a few charts up with some key sets of hypergeometric distributions on them for reference purposes.
If you would like to know more about hypergeometric distributions or you would like to see more posts like this, let me know by subscribing to my blog and leaving a comment. Good luck out there.
The guys covering Pro Tour Philadelphia made an interesting point. The metagame shaped up very similar to what was being seen online before the event. This is unusual, as MTGO standard and paper standard are usually quite different. As one reason for this, combo decks have a real weakness in MTGO. Having to actually go infinite can be the death of certain types of combo decks online. In paper magic, you can just perform the combo five times and then say some impossibly large number. I sincerely wish they had posited a reason for this. Could it be that more competitive Magic players are getting into MTGO and qualifying for Pro Tour events that way, or was it just a fluke?
Another factor is the availability of cards and their prices. MTGO is always in flux and card prices stabilize very quickly. Card prices take a lot longer to stabilize in paper Magic because transactions take a whole lot longer, and cards cannot be moved between 5 different merchants in one minute. Keeping an eye on where MTGO prices are going on certain cards can be an excellent strategy for determining where card prices are headed in the near future, particularly if they are cards that fit into competitive decks. Availability is a large component to the appeal of MTGO. One can check the card prices of hundreds of merchants in a matter of minutes rather than hours. Also, access to any card you could ever want that is in print on MTGO are at your fingertips.
With decks like Caw-Go, Mono-White Quest, and Vengevine just a few weeks from rotating out of standard, a number of decks will need to fill the void. One mentioned by channelfireball.com is a little Puresteel Paladin brew. You can view the decklist here, along with a few sample games. As mentioned, the deck has some real consistency issues. Another list on StarCity Games had a different take. View it here. The deck has an interesting inclusion I really like: the 1-of Glint Hawk. The card allows you to reuse your Mortarpods without sacrificing another creature. It also draws a card off of Puresteel Paladin if you bounce an equipment with it and re-play it. To replace the Squadron Hawks in the channelfireball version, this deck has another few interesting features: 2 Kor Firewalkers and an extra Etched Champion. With a little tuning, the deck should have some serious game.
Timely Reinforcements can be a beating in the right deck. The card reminds me of another 3-mana card that saw play in W/B tokens back when Cruel Control was “the” deck in standard: Spectral Procession. Though the card has a pretty hefty drawback (needing to have fewer creatures than an opponent, less life), it seems rather swingy, especially surrounded by Battle Cry effects. Control decks can make very effective use of this card as well. Casting this the turn before a lethal alpha strike from Signal Pest and company, netting another turn of life, could mean the difference between stabilizing at 1 through a wrath effect or dying outright. Even if the card produces three guys or nets 6 life, the dire situation may necessitate it, and it may be enough to do the job.
Something else to consider when evaluating this card is that Hideaway lands have been out of standard for a looooooong time now. The hideaway lands really powered the W/B tokens deck in many respects, as it allowed the deck to power out some heavy hitters at a very substantial discount.
Will the card find a home in a deck? Probably. I don’t foresee anyone passing up on this kind of effect. Will it be a format-defining staple like Path to Exile, Spectral Procession, or the like? Probably not. The card isn’t quite good enough. A mono-white midrange deck that exploits Battle Cry may find the card useful, but its drawback will likely be its downfall. Strike two against the card is that it really doesn’t fit into Tempered Steel.dec (now watch me be horribly wrong). Battle Cry is an interesting mechanic that will see professionals tuning decks that include it. In fact, we are already seeing this to some extent. Contested War Zone, Hero of Bladehold, Hero of Oxid Ridge, and Signal Pest have all had top 8 appearances.
Quest decks may want to look into the card as well. Doh! Nevermind. We are a few weeks from the Innistrad release.